考虑气压效应的浅埋隧道开挖影响解析解答

 基于隧道开挖椭圆化变形模式，针对盾构施工分别考虑气压效应与无气压效应2种工况，提出饱和土中浅埋隧道开挖引起的地层长、短期变形和隧道衬砌内力位移的计算方法。结果表明：椭圆化变形模式下得到的位移曲线与实测值吻合较好，考虑气压效应条件下隧道开挖施工引起的土体变形大于非气压工况，长期影响解大于短期影响解。通过参数调整研究衬砌洞周处位移分布规律时，发现衬砌径向负位移在90°拱顶处达到最大值，在270°拱底处取得最小值，反映了衬砌明显的椭圆化和整体下沉变形趋势，并且随着半径增大以及土体模量减小，椭圆化变形趋势越明显；切向位移值基本以90°/270°隧道中轴线为分界轴，正值取在隧道左半圆，负值取在隧道右半圆，增大半径以及减小土体模量提高了切向位移值的整体水平。通过参数调整研究衬砌内力分布规律时，发现硬土质和大间隙时隧道轴力更容易表现出明显的椭圆化分布趋势，弯矩值随着隧道埋深、隧道半径以及土体重度减小而减小，随着土体侧压力系数k的减小而增大。盾构气压水平的提升，使衬砌轴力受压区范围增幅明显，并使衬砌的正、负弯矩值均增大。分析成果可为正确预估复杂工况下盾构开挖变形提供一定的理论依据。

Closed-form solution of excavation effects induced by shallow tunnel considering air pressure

A method to calculate the long-term and short-term soil displacements and liner stress affected by tunneling in saturated ground was proposed based on the oval deformation mode under two conditions of excavation with or without air pressure. It was observed that the soil deformation curves under the oval deformation mode are in good agreements with the measured values. The excavation under air pressure generates a larger soil deformation than under the non-pressure condition. The long-term settlements in saturated ground are larger than the short-term ones. The variation of the displacement of liner in saturated ground was investigated through parametric analysis. The results show that the maximum negative value of radial displacement of liner occurs at 90° while the minimum one at 270°，which reflects a significant oval deformation trend and overall subsidence. With the increase of the radius and the decrease of the soil moduli，the deformation trend becomes more obviously. The tangential displacement takes the axis of 90°/270° as the boundary axis，and the positive value is obtained at left semicircle while the negative value is obtained at right semicircle. Increasing the radius and decreasing the soil moduli raise the overall level of tangential displacement values. Investigations on the stress of liner through parametric analysis，indicate that the axial force is more likely to present a clear elliptical deformation trend when the tunnel gets stiffer ground or larger gap. The bending moment becomes smaller with the decrease of the depth，the radius and the weight of the soil. The bending moment becomes larger with the decrease of lateral earth pressure coefficient k. The increasing of air pressure results in the rise of the range of compression zone and the values of both positive and negative bending moments.